In case you haven’t heard, the St. Louis Rams are running a contest to predict the team’s 2014 schedule. lThe prize is $100,000, which sounds nice until you realize that to win, you must accurately predict not only the opponent each week, but the location and the exact day of the game. Nobody is going to win this contest. Nobody is going to come close to winning the contest. It’s a personal information/PR grab and nothing more. Normally, this wouldn’t bother me, but it’s not like the Rams are giving away a billion dollars. For a hundred grand — which is less than two percent of the amount of dead cap space being allocated to Cortland Finnegan this season — the team shouldn’t have needed to make it impossible for anybody to win. Considering the rules, St. Louis might as well have announced that the grand prize is eleventy billion dollars.

So what are the odds of winning this contest? Let’s start with an easier problem than the one at hand: predicting the Rams opponent in each week of the season.

With 17 weeks, there are 17 possible opponents once you include home/road designations and the bye week. Therefore, you have a 1-in-17 chance of correctly guessing the Rams opponent in week one. By extension, you have a 1-in-16 chance of correctly guessing who St. Louis plays in week two, assuming you were correct with your guess in week one (this is what we mean by conditional probabilities). Do this for every week of the season, and by week 17, you have a 100% chance of correctly guessing who is on the team’s schedule.

It may not be intuitive exactly how daunting a task this is. But this is much, much harder than Warren Buffet’s bracket contest. For example, you only have a a 1-in-272 chance of correctly guessing who the Rams opponents will be in the first two weeks of the season. That drops to 1-in-4,080 through three weeks, 1-in-8.9 million through six weeks, and 1-in-8.8 billion through nine weeks. That already makes it harder than the bracket contest, and you still have the back eight to play. The odds of correctly guessing the opponent each week is 1-in-356 trillion. And remember, this is quite a bit easier than the actual contest!

But let’s make some adjustments based on the information we know (which will lower the odds) and the added conditions one must satisfy (which will drastically increase the odds).

Adjustment #1

The first adjustment to our 1-in-356 trillion likelihood lowers the odds. If we assume that each team plays a division opponent in week 17, that makes the contest ever so slightly easier. If we work in reverse order, you now have a 1-in-6 chance of guessing the week 17 opponent (remember, you need to specify game location), a 1-in-16 chance of guessing the week 16 opponent assuming your week 17 selection was correct, and so on. This improves your odds all the way to 1-in-126 trillion. Hooray?

Adjustment #2

One more adjustment to make the probability ever so slightly more favorable. The bye weeks are a moving target for the NFL, but last year, they were limited to weeks 4 through 12. Since we’re dealing with infinitesimal odds, let’s just make life easy on ourselves and assume 1) the bye weeks will again occur only during those weeks and 2) the Rams have an equally likely chance of having a bye on each of those nine weeks.

Let’s assume you have a 1-in-9 chance of correctly guessing the bye week. Putting that aside, you then have a 1-in-6 chance of predicting the week 17 game, a 1-in-15 chance of predicting week 16, a 1-in-14 of predicting week 15, and so on. Multiply all the conditional probabilities, and this increases your odds to 1 in 70.6 trillion.1

Adjustment #3

Apparently, the actuaries at the insurance company St. Louis surely hired determined that a 1-in-70 trillion chance was leaving too just much skin in the game. Because the rules provide that you also need to determine the day of the week for each game!

We can assume Sundays for most games, but that still leaves a few odd weeks you need to guess correctly. Consider:

Last season there were 17 games on Thursday nights spread over 15 weeks (remember, there are three on Thanksgiving). If the same pattern is followed this year (and I don’t even know if that’s the case), that means there’s a 1-in-16 chance the Rams will play two Thursday night games. And since the Seahawks will play in the opener, there’s also a 1-in-8 chance St. Louis could play in the opener. But let’s make the math easy on ourselves and make two assumptions:

St. Louis will only play one Thursday game in 2014.

That game is equally likely to occur in any of weeks 1 through 15.

Therefore, you have a 1-in-15 chance of guessing which week St. Louis will play on Thursday night. This takes our odds to 1-in-1.6 quadrillion.

Next, we need to predict the number of Monday Night games for St. Louis. Odds are, it will be zero or one games: after all, the Rams have played in just three Monday night games over the last five years. One can’t get very precise with estimating the likelihood of Monday night games the Rams will play, but I think the best guess would be to assume one (i.e., that would be the mode if the schedule was played out 10,000 times). The Monday night game can occur in any of the first 16 weeks except the week the Rams play on Thursday night; as a result, this 1/15 probability jumps our odds to 1-in-16 quadrillion. But if we assume there is only a 50% chance the Rams play exactly one Monday Night game this year,2 the odds double to 1-in-32 quadrillion.

But wait, there’s more! Four teams will play on Saturday in week 16 this year, December 20th. So there is a 28/32 chance the Rams will not play a Saturday game: that ups our odds to 1-in-36 quadrillion.

With a grand prize of just $100,000, this has to be in the running for worst contest ever. The expected value upon entering the contest is $0.0000000000028. It is literally not worth a second of your time to enter this contest.

For the Rams, though, the contest offers some nice benefits. St. Louis will receive some positive PR, particularly among those who are not mathematically-inclined. And to enter, one has to provide the Rams with their home address, email address and phone number, valuable information for the St. Louis marketing department. So this is certainly a good deal for the Rams.

But for the contestant? There’s simply no point in entering. As a practical matter, there isn’t even a grand prize (note: there is only one prize, but that doesn’t stop the Rams from publicizing this as the “grand prize”). That’s because the contest rules provide that anyone involved in the determination of or release of the 2014 NFL Schedule, or with any advance direct or incidental knowledge of the actual 2014 NFL schedule, is not eligible to participate in the contest. As a result, any entry submitted by such an individual will be void and ineligible to claim any prize award.

2) Use “script, macro or automated devices (or any other devices intended to automate or subvert any aspect of entry)” to give yourself more than one entry. This is expressly prohibited, and any entry through such means will be declared void.

Think about this for a second. In my unfounded opinion (ATTN: Rams lawyers), if you enter this contest and predict the Rams exact schedule, you are much, much, much more likely to wind up in a lawsuit than you are the winner of $100,000.

Another way you get to this result: a 1/6 chance in week 17, a 1/15 chance in week 16, a 1/14 chance in week 15, 1/13 in week 14, a 1/12 in week 13, a 1/11 in week 1, a 1/10 in week 2, and a 1/9 in week 3. Then, you have a 1/9 chance in week 4 (since the bye is now in play), a 1/8 in week 5, and so on until you get a 1/1 chance in week 12. [↩]

Only three of the last ten years have the Rams played exactly one Monday Night game. [↩]

Wow, that really is a terrible contest. I guess there’s two possibilities for the Rams: 1) They’re worried about cheating or 2) Nobody did/understood the math. I lean towards the latter.

Richie

the actuaries at the insurance company St. Louis surely hired determined that a 1-in-70 trillion chance was leaving too just much skin in the game.

I almost spit up my coffee when I read that!

Richie

CBS will air eight early-season games before NFL Network takes the baton for eight late-season games leading up to the playoffs. Fourteen games will be played Thursday, with two late-season games taking place Saturday.

Plus, I assume, CBS and FOX will each have a game on Thanksgiving.

Then this means that either:
a) NBC doesn’t get the Week 1 Thursday game
b) There will be a Thursday game every week (Week 1 – NBC, Week 2-9 – CBS, Week 10-17 – NFL)

Speaking of odds, what are the odds that two of the greatest quarterbacks of all time would have the middle name Constantine?

Loyd Christmas

So your saying there’s a chance?

Ian

The odds aren’t quite as small as that. I believe the NFL never has teams play more than two road/home games than home/road games at any point in the season. Thus, instead of 16 choose 8 = 12,780 possibilities for the home-road order, there are only 2*3^(8-1) = 4,374 possibilities, or about a third as many. That should roughly increase the odds to 1-in-12 quadrillion. And then there are other scheduling tendencies that you can use, such as never playing the same division opponent on consecutive weeks to push the odds ever so slightly up.

Chase Stuart

Thanks, Ian. Good points. Although even if you up the odds to say, 1 in 1 quadrillion, you’re still looking at an expected value of $0.0000001 for entering the contest. If someone wins, we can be almost certain that they cheated and therefore are ineligible, rather than assume that they legitimately won.

Also, assuming a 1-in-1 quadrillion chance… and assuming 100,000 people enter the contest (probably a very optimistic guess)…. and assuming their entries are independent (obviously not true)…. there is a 99.99999000022170%% chance that there will not be a winner, or roughly a 1 in 10 million chance that nobody wins the contest. So for a 1-in-10M chance, the Rams are giving away $100,000. I can’t imagine the insurance premium was very high on this contest.

JeremyDe

I thought the same thing about not scheduling 2+ consecutive home/road games, but I remembered seeing it last year. After a quick look at the schedule, it happened 10 times last year (12 if you don’t count bye weeks). The Titans got the worst/best of it. 3 homes from Week 3-5 and 3 road 12-14. Not sure if there was some strange scheduling anomaly going on last year, or if the NFL has been doing this for a while with little notice.

Also, for the problem of the original contest, wouldn’t the location only matter for the division games? I think the NFL schedule matrix sets the location for the non-division games, so teams know where they are playing non-division opponents, just not when.

I didn’t look at the contest, had no interest from the start, do you have to differentiate between the game times? Sunday afternoon vs Sunday night? IF so, how p*ssed would you be to get 15 games correct and they flexed out a Rams game!

JeremyDe

It was only opponent, location, and day of the week, not game time. It was also about the original released schedule. If someone was flexed later, it wouldn’t matter. Still impossible odds.